Generators (Scatter Plots)

Notebook for generating basic scatter plots of the Pareto-optimal fronts with appropriate colorings and point-sizes.

This notebook can be used to generate basic scatter plots of all the Pareto-optimal fronts with suitable colorings and point-sizes. All the Pareto-optimal data point files hard-coded in the dictionary pfs. Currently this notebook provides these Pareto-optimal fronts.

  • DTLZ2 ($m$-Sphere) Problem
  • DEBMDK (Knee) Problem
  • CDEBMDK (Constrained Knee) Problem
  • C0-DTLZ2 (A split $m$-sphere with a small isolated cluster at $f_m$-axis)
  • C2-DTLZ2 Problem
  • DTLZ8 Problem (A 3-dimensional line and an $m$-dimensional hypersurface)
  • GAA Problem (A 10-objective and 18-constraint general aviation design problem)
In [1]:
%matplotlib notebook
%reload_ext autoreload
%autoreload 2

import sys
import os

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
import matplotlib.colors as mc
from mpl_toolkits.mplot3d import Axes3D

plt.rcParams.update({'figure.max_open_warning': 0})

Generate and save plots.

In [2]:
sys.path.append('../')
from vis.utils import io
from vis.utils import transform as tr

def load_props(path):
    r"""
    Load CV, Mu, Ik and S from path.
    """
    CV = None
    cvpathf = os.path.join(path, "datacv.csv")
    if os.path.exists(cvpathf):
        CV = np.loadtxt(cvpathf)

    # load the Mu values
    Mu = None
    mupathf = os.path.join(path, "mu.csv")
    if os.path.exists(mupathf):
        Mu = np.loadtxt(mupathf)

    # load the knee indices
    Ik = None
    kpathf = os.path.join(path, "muid.csv")
    if os.path.exists(kpathf):
        Ik = np.loadtxt(kpathf, dtype = int)
        
    return CV, Mu, Ik

def decide_size_color(CV, Mu, Ik):
    r"""
    Decide point-size and color from `CV`, `Mu` and `Ik`
    """
    # decide point-size
    S = 1
    if Mu is not None and Ik is not None:
        S = tr.resize_by_tradeoff(Mu, k = Ik)

    # decide colors
    # C = tr.default_color(F.shape[0], alpha = 0.5)
    M = np.mean(F, axis = 0)
    C = tr.color_by_dist(F, M)
    
    # if CV is available, use CV to color
    if CV is not None:
        C = tr.color_by_cv(CV)

    # enhance knee points
    if Ik is not None:
        C = tr.enhance_color(C, Ik)
    return S, C
In [3]:
pfs = {'dtlz2': ['3d', '4d', '8d'], \
       'dtlz2-nbi': ['3d', '4d', '8d'], \
       'debmdk': ['3d', '4d', '8d'], \
       'debmdk-nbi': ['3d', '4d', '8d'], \
       'debmdk-all': ['3d', '4d', '8d'], \
       'debmdk-all-nbi': ['3d', '4d', '8d'], \
       'dtlz8': ['3d', '4d', '6d', '8d'], \
       'dtlz8-nbi': ['3d', '4d', '6d', '8d'], \
       'c2dtlz2': ['3d', '4d', '5d', '8d'], \
       'c2dtlz2-nbi': ['3d', '4d', '5d', '8d'], \
       'cdebmdk': ['3d', '4d', '8d'], \
       'cdebmdk-nbi': ['3d', '4d', '8d'], \
       'c0dtlz2': ['3d', '4d', '8d'], \
       'c0dtlz2-nbi': ['3d', '4d', '8d'], \
       'crash-nbi': ['3d'], 'crash-c1-nbi': ['3d'], 'crash-c2-nbi': ['3d'], \
       'gaa': ['10d'], \
       'gaa-nbi': ['10d']}

for pf in list(pfs.keys()):
    for dim in pfs[pf]:
        fullpathf = "../data/{0:s}/{1:s}/dataf.csv".format(pf, dim)
        if os.path.exists(fullpathf):
            path, filenamef = os.path.split(fullpathf)
            dirs = path.split('/')
            frontname = dirs[-2]

            # load the front
            F = np.loadtxt(fullpathf, delimiter = ',')
            print(fullpathf, F.shape, dirs, frontname)
            
            CV, Mu, Ik = load_props(path)
            S,C = decide_size_color(CV, Mu, Ik)
            
            figpath = os.path.join(path, "scatter3d.pdf")
            with plt.rc_context({"text.usetex": True, "font.size": 12}):
                fig = plt.figure()
                ax = Axes3D(fig)
                ax.xaxis.set_rotate_label(False)
                ax.yaxis.set_rotate_label(False)
                ax.zaxis.set_rotate_label(False)

                ax.set_xlabel(r"$f_1$")
                ax.set_ylabel(r"$f_2$")
                ax.set_zlabel(r"$f_3$")
                ax.scatter(F[:,0], F[:,1], F[:,2], color = C, s = S)

                # save the fig
                plt.savefig(figpath, bbox_inches = 'tight', pad_inches = 0, dpi = 150)

                plt.show()
../data/dtlz2/3d/dataf.csv (1000, 3) ['..', 'data', 'dtlz2', '3d'] dtlz2
../data/dtlz2/4d/dataf.csv (2000, 4) ['..', 'data', 'dtlz2', '4d'] dtlz2
../data/dtlz2/8d/dataf.csv (4000, 8) ['..', 'data', 'dtlz2', '8d'] dtlz2
../data/dtlz2-nbi/3d/dataf.csv (990, 3) ['..', 'data', 'dtlz2-nbi', '3d'] dtlz2-nbi
../data/dtlz2-nbi/4d/dataf.csv (1771, 4) ['..', 'data', 'dtlz2-nbi', '4d'] dtlz2-nbi
../data/dtlz2-nbi/8d/dataf.csv (3432, 8) ['..', 'data', 'dtlz2-nbi', '8d'] dtlz2-nbi
../data/debmdk/3d/dataf.csv (1047, 3) ['..', 'data', 'debmdk', '3d'] debmdk
../data/debmdk/4d/dataf.csv (1967, 4) ['..', 'data', 'debmdk', '4d'] debmdk
../data/debmdk/8d/dataf.csv (4077, 8) ['..', 'data', 'debmdk', '8d'] debmdk
../data/debmdk-nbi/3d/dataf.csv (1143, 3) ['..', 'data', 'debmdk-nbi', '3d'] debmdk-nbi
../data/debmdk-nbi/4d/dataf.csv (2028, 4) ['..', 'data', 'debmdk-nbi', '4d'] debmdk-nbi
../data/debmdk-nbi/8d/dataf.csv (3432, 8) ['..', 'data', 'debmdk-nbi', '8d'] debmdk-nbi
../data/debmdk-all/3d/dataf.csv (1000, 3) ['..', 'data', 'debmdk-all', '3d'] debmdk-all
../data/debmdk-all/4d/dataf.csv (2000, 4) ['..', 'data', 'debmdk-all', '4d'] debmdk-all
../data/debmdk-all/8d/dataf.csv (4000, 8) ['..', 'data', 'debmdk-all', '8d'] debmdk-all
../data/debmdk-all-nbi/3d/dataf.csv (990, 3) ['..', 'data', 'debmdk-all-nbi', '3d'] debmdk-all-nbi
../data/debmdk-all-nbi/4d/dataf.csv (1771, 4) ['..', 'data', 'debmdk-all-nbi', '4d'] debmdk-all-nbi
../data/debmdk-all-nbi/8d/dataf.csv (3432, 8) ['..', 'data', 'debmdk-all-nbi', '8d'] debmdk-all-nbi
../data/dtlz8/3d/dataf.csv (1038, 3) ['..', 'data', 'dtlz8', '3d'] dtlz8
../data/dtlz8/4d/dataf.csv (2105, 4) ['..', 'data', 'dtlz8', '4d'] dtlz8
../data/dtlz8/6d/dataf.csv (2659, 6) ['..', 'data', 'dtlz8', '6d'] dtlz8
../data/dtlz8/8d/dataf.csv (3680, 8) ['..', 'data', 'dtlz8', '8d'] dtlz8
../data/dtlz8-nbi/3d/dataf.csv (1025, 3) ['..', 'data', 'dtlz8-nbi', '3d'] dtlz8-nbi
../data/dtlz8-nbi/4d/dataf.csv (2088, 4) ['..', 'data', 'dtlz8-nbi', '4d'] dtlz8-nbi
../data/dtlz8-nbi/6d/dataf.csv (3535, 6) ['..', 'data', 'dtlz8-nbi', '6d'] dtlz8-nbi
../data/dtlz8-nbi/8d/dataf.csv (2277, 8) ['..', 'data', 'dtlz8-nbi', '8d'] dtlz8-nbi
../data/c2dtlz2/3d/dataf.csv (1086, 3) ['..', 'data', 'c2dtlz2', '3d'] c2dtlz2
../data/c2dtlz2/4d/dataf.csv (2088, 4) ['..', 'data', 'c2dtlz2', '4d'] c2dtlz2
../data/c2dtlz2/5d/dataf.csv (2098, 5) ['..', 'data', 'c2dtlz2', '5d'] c2dtlz2
../data/c2dtlz2/8d/dataf.csv (4305, 8) ['..', 'data', 'c2dtlz2', '8d'] c2dtlz2
../data/c2dtlz2-nbi/3d/dataf.csv (1036, 3) ['..', 'data', 'c2dtlz2-nbi', '3d'] c2dtlz2-nbi
../data/c2dtlz2-nbi/4d/dataf.csv (1984, 4) ['..', 'data', 'c2dtlz2-nbi', '4d'] c2dtlz2-nbi
../data/c2dtlz2-nbi/5d/dataf.csv (2280, 5) ['..', 'data', 'c2dtlz2-nbi', '5d'] c2dtlz2-nbi
../data/c2dtlz2-nbi/8d/dataf.csv (3872, 8) ['..', 'data', 'c2dtlz2-nbi', '8d'] c2dtlz2-nbi
../data/cdebmdk/3d/dataf.csv (1099, 3) ['..', 'data', 'cdebmdk', '3d'] cdebmdk
../data/cdebmdk/4d/dataf.csv (1982, 4) ['..', 'data', 'cdebmdk', '4d'] cdebmdk
../data/cdebmdk/8d/dataf.csv (3919, 8) ['..', 'data', 'cdebmdk', '8d'] cdebmdk
../data/cdebmdk-nbi/3d/dataf.csv (1049, 3) ['..', 'data', 'cdebmdk-nbi', '3d'] cdebmdk-nbi
../data/cdebmdk-nbi/4d/dataf.csv (2042, 4) ['..', 'data', 'cdebmdk-nbi', '4d'] cdebmdk-nbi
../data/cdebmdk-nbi/8d/dataf.csv (3380, 8) ['..', 'data', 'cdebmdk-nbi', '8d'] cdebmdk-nbi
../data/c0dtlz2/3d/dataf.csv (1002, 3) ['..', 'data', 'c0dtlz2', '3d'] c0dtlz2
../data/c0dtlz2/4d/dataf.csv (2003, 4) ['..', 'data', 'c0dtlz2', '4d'] c0dtlz2
../data/c0dtlz2/8d/dataf.csv (4005, 8) ['..', 'data', 'c0dtlz2', '8d'] c0dtlz2
../data/c0dtlz2-nbi/3d/dataf.csv (983, 3) ['..', 'data', 'c0dtlz2-nbi', '3d'] c0dtlz2-nbi
../data/c0dtlz2-nbi/4d/dataf.csv (1916, 4) ['..', 'data', 'c0dtlz2-nbi', '4d'] c0dtlz2-nbi
../data/c0dtlz2-nbi/8d/dataf.csv (3180, 8) ['..', 'data', 'c0dtlz2-nbi', '8d'] c0dtlz2-nbi
../data/crash-nbi/3d/dataf.csv (4450, 3) ['..', 'data', 'crash-nbi', '3d'] crash-nbi
../data/crash-c1-nbi/3d/dataf.csv (711, 3) ['..', 'data', 'crash-c1-nbi', '3d'] crash-c1-nbi
../data/crash-c2-nbi/3d/dataf.csv (3739, 3) ['..', 'data', 'crash-c2-nbi', '3d'] crash-c2-nbi
../data/gaa/10d/dataf.csv (3112, 10) ['..', 'data', 'gaa', '10d'] gaa
../data/gaa-nbi/10d/dataf.csv (3112, 10) ['..', 'data', 'gaa-nbi', '10d'] gaa-nbi
In [ ]: